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SUMMARY:Course: Reaction-diffusion eqs and the evolution of dispersal (K.-
Y. Lam) on Mondays 14h-16h
DTSTART;VALUE=DATE-TIME:20220117T130000Z
DTEND;VALUE=DATE-TIME:20220325T150000Z
DTSTAMP;VALUE=DATE-TIME:20220118T132412Z
UID:indico-event-6547@indico.math.cnrs.fr
DESCRIPTION:Back to main page\n\nIn this course\, we introduce some basic
tools and discuss some recent progress of reaction-diffusion models motiva
ted spatial ecology and evolution. This course will start by reviewing som
e basic theory of elliptic and parabolic estimates. The main content consi
sts of three parts. \n\nThe first part concerns the single species model\
, covering persistence\, critical domain size\, global attractivity of pos
itive solutions.Basics of the theory monotone dynamical systems\; princi
pal eigenvalue of elliptic/parabolic equations will be introduced.\n\nThe
second part concerns the competition of multiple species. We will discuss
the competition model introduced in [Dockery et al.\, J. Math. Biol. (199
8)] and discuss their proof of the case of two species in detail\, and the
ir conjecture regarding the Morse decomposition of the N species case. We
will then discuss recent progress on N specie. We also introduce the conce
pt of evolutionarily stable strategies and other notions from adaptive dyn
amics\, and discuss related results for stream populations. Basics of the
theory of principal Floquet bundle\, and elements from dynamical systems w
ill be discussed.\n\nThe third part concerns a mutation-selection model in
troduced in [Diekmann et al.\, Theor. Pop. Biol\, (2005)] concerning th
e competition of infinitely many species. We will discuss the result in [
Perthame and Souganidis\, Math. Model. Nat. Phenom. (2016)] concerning st
ationary solutions\, and related results in stream populations [Hao et al.
Indiana Univ. Math. J. (2019)]. We will also discuss recent progress on t
he time-dependent problem\, including the uniqueness in constrained Hamilt
on-Jacobi equations [Calvez et al.\, Cal. Var. Par. Diff. Eq.\, (2020)].\n
\nMost of the course will be self-contained and is aimed at graduate stude
nts with knowledge at masters level real analysis.\n\nhttps://indico.math.
cnrs.fr/event/6547/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6547/
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